Under the Affordable Care Act, the federal government covers all initial costs for states to expand their Medicaid programs up to 133 percent of the federal poverty line.
Arizona's program currently covers most people below the U.S. poverty level, meaning about 300,000 would gain coverage if the state expands Medicaid.
Brewer has consistently locked horns with Obama on immigration policy, leading to a confrontation between the two on a Phoenix airport tarmac in Jan. 2012.
A Tea Party favorite, Brewer has also been a strong critic of the healthcare law. But she reportedly said Monday that last summer's Supreme Court ruling and Obama's re-election mean the law is here to stay.
Brewer also argued that uncompensated emergency room care levies a "hidden tax" of $2,000 on Arizona families, according to a report.
The Supreme Court's decision to uphold the Affordable Care Act made the law's Medicaid expansion optional for states.
Most Republican governors have refused to add additional low-income people to the program, citing cost concerns.